## The Taylor Funct

##### Copyright 1995 by Jeff Suzuki

Note: if you can't figure out the tune to this song and the proper
pronunciation of the word "funct" after the first verse, you had a
very fortunate childhood. As with the log song, all the mathematics
are correct. (a_n means a with subscript n; it should just be read "a
n".) If someone out there knows of a way to get subscripts and
superscripts, I'd love to hear how: email me at jeffs@math.bu.edu

Here's the story

Of a power series

a_n over n factorial x to the n

Where the a_n's are just deriv'tives

With a zero plugged in.

Here's the story

Of the remainder

Which is just like the next term that you should get

But instead of inputting zero

Plug in c instead.

One day this R_n met this series

And they knew that it was much more than a hunch

That if R_n should tend to zero

The series would approach the funct.

The Taylor funct.

The Taylor funct.

That's the way we derive the Taylor funct!

Choose another awful song

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